不定积分的题 期末复习中
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(1)
f(x)=x^5.cosx
f(-x)=-f(x)
=>∫(-2->2) x^5.cosx dx =0
(2)
f(x) = (cosx)^4
f(-x) =f(x)
∫(-π/2->π/2) (cosx)^4 dx
=2∫(0->π/2) (cosx)^4 dx
=(1/2)∫(0->π/2) (1+cos2x)^2 dx
=(1/2)∫(0->π/2) [1+2cos2x + (cos2x)^2 ] dx
=(1/4)∫(0->π/2) [3+4cos2x + cos4x ] dx
=(1/4) [ 3x + 2sin2x +(1/4)sin4x] |(0->π/2)
=(3/8)π
f(x)=x^5.cosx
f(-x)=-f(x)
=>∫(-2->2) x^5.cosx dx =0
(2)
f(x) = (cosx)^4
f(-x) =f(x)
∫(-π/2->π/2) (cosx)^4 dx
=2∫(0->π/2) (cosx)^4 dx
=(1/2)∫(0->π/2) (1+cos2x)^2 dx
=(1/2)∫(0->π/2) [1+2cos2x + (cos2x)^2 ] dx
=(1/4)∫(0->π/2) [3+4cos2x + cos4x ] dx
=(1/4) [ 3x + 2sin2x +(1/4)sin4x] |(0->π/2)
=(3/8)π
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